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https://dictionary.cambridge.org/dictionary/english/go-off

on the above address you can see:

It's getting cold. The heater must have gone off.

why there is "have" instead of "has"? isn't "the heater" a singular noun?

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    Note that the phrase "gone off" is more commonly used to describe something being triggered, like a bomb or an alarm clock. As an native speaker, I would tend to say, "The heater must have shut off" (or "...turned off").
    – GentlePurpleRain
    Commented Jan 23 at 17:34
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    I know this wasn't the focus of your question, but following up on @GentlePurpleRain's comment, as a native Canadian/US English speaker, I believe the verb phrase "go off" is rarely used in US or Canadian English in sense B1 from that link ("If a light or a machine goes off, it stops working"). In the US and Canada, lights and power usually go out. Heaters or machines either shut off or turn off. For example, "The heater must have shut off when the power went out."
    – K. A. Buhr
    Commented Jan 23 at 21:31
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    In British English the phrase "gone off" to mean turned off is very common. As a native British English speaker I have said "it's getting cold, the [central] heating must have gone off" many times recently.
    – Nibor
    Commented Jan 23 at 22:05
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    Shut off is almost unknown in British English in this sense, and turn off is much more common as a causative ("I turned the heater off") than as a middle ("The heater turned off"). The heater turned itself off is possible, but (particularly as a perfect) The heater's gone off seems to me by far the most likely.
    – Colin Fine
    Commented Jan 23 at 23:03
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    Its more "Turned off" than "Gone off". "Gone off" may also mean the start of things, like "The start of the race had gone off to a whimper of a start"
    – Richie
    Commented Jan 24 at 1:03

2 Answers 2

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"must" is a modal verb, and the verb following a modal is always in the base or "bare infinitive" form.

He should be ...

She can play ...

It must have gone off.

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-4

No, because "gone off" is colloquially used to indicate an explosion.

In this context, you want something like "the heater must have turned itself off".

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    Using "gone off" to mean turned off is common in British English, much less so in US and Canadian English.
    – Nibor
    Commented Jan 23 at 22:08
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    I'm British. It's not.
    – Mark Morgan Lloyd
    Commented Jan 23 at 22:09
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    I'm British and use it regularly, maybe it's a regional thing. "I was late for work because my alarm didn't go off" and "the heating has gone off" are two phrases I've used recently.
    – Nibor
    Commented Jan 23 at 22:17
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    In any case, the poster's question is not about the meaning - it's about why it's "must have" rather than "must has". The phrase they quote comes from the Cambridge dictionary (see the link in the question).
    – James Martin
    Commented Jan 23 at 22:27
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    This answer is looking at the wrong thing. This has nothing to do with "gone off", as "The heater has gone off" is a perfectly valid construction. The issue here is with the introduction of "must". The exact same principle applies in cases where "gone off" is not used, e.g. "he must have forgotten" or "she must have been killed".
    – Flater
    Commented Jan 23 at 23:27

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